Y is inversely proportional to x, when Y = 2, x = 4.

Find the value of x when Y = 4.

65 sequences.

Lets solve the problem,

The last term is 0.

To form the first 18 terms, we must combine the following two sequences:

0-1 and 0-1-1

Any combination of these two sequences will yield a valid case in which no two 0's and no three 1's are adjacent

So we will combine identical 2-term sequences with identical 3-term sequences to yield a total of 18 terms, we get:

2x + 3y = 18

Case 1: x=9 and y=0

Number of ways to arrange 9 identical 2-term sequences = 1

Case 2: x=6 and y=2

Number of ways to arrange 6 identical 2-term sequences and 2 identical 3-term sequences =8!6!2!=28=8!6!2!=28

Case 3: x=3 and y=4

Number of ways to arrange 3 identical 2-term sequences and 4 identical 3-term sequences =7!3!4!=35=7!3!4!=35

Case 4: x=0 and y=6

Number of ways to arrange 6 identical 3-term sequences = 1

Total ways = Case 1 + Case 2 + Case 3 + Case 4 = 1 + 28 + 35 + 1 = 65

Hence the number of sequences are 65.

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The machine produces 3000 nails in the month of April 2007.

Production of Nails in the Month of April

According to the given information,

Number of nails manufactured per day by the machine, x = 300  

And, we know that April is the fourth month of a year which has total 30 days.

Hence, number of days the machine is manufacturing nails in the month of April, y = 30

So, the number of nails that will be produced by the machine in the month of April is given by,

N = Number of nails produced per day × Number of days in April

N = xy

N = 300 × 30

N = 9000

Therefore, the machine produces 9000 nails in the April month of year 2007.

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Answer:

M: 74.579° = 74°34'43" = 1.30164

O: 49.421° = 49°25'17" = 0.86256 rad

Answer:

[tex]\frac{13\pi }{9}[/tex] radians

Step-by-step explanation:

to convert degrees to radians

degrees × [tex]\frac{\pi }{180}[/tex]

= 260 × [tex]\frac{\pi }{180}[/tex]

= 26 × [tex]\frac{\pi }{18}[/tex]

= 13 × [tex]\frac{\pi }{9}[/tex]

= [tex]\frac{13\pi }{9}[/tex]

Answer:

c 1:4

Step-by-step explanation:

The correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.

The square inches of paper needed A = surface area of cone +  area of overlap

The surface area of the cone is given by A = πr[r + √(h² + r²)] where

So, A = πr[r + √(h² + r²)]

A = π × 2 × [2 + √(6² + 2²)]

A = π × 2 × [2 + √(36 + 4)]

A = π × 2 × [2 + √40]

A = π × 2 × [2 + 2√10]

A = 2π[2 + 2√10]

A = 4π + 4π√10

The area of overlap A' = wL where

So, A' = wL

A' = w[√(h² + r²)]

A' =  1/2[√(6² + 2²)]

A' =  1/2[√(36 + 4)]

A' =  1/2[√40]

A' =  1/2 × 2√10

A' = √10

So, the number of square inches of paper needed is A" = A + A'

=  4π + 8π√10 + √10

Since the number of square inches of paper needed is 4π + 4π√10 + √10

So, the correct statements are Neither was correct and Joe used the height and radius to calculate the slant height.

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Answer:

Its A or B

Step-by-step explanation:

44% is the answer

6 Article price at buying =5 Rs

1 Article price at buying = 5/6...(i)

5 Articles sold at Rs. 6

1 Articles cost at sold = 6/5 ....(ii)

% Gain=((6/5 - 5/6)/ 5/6) * 100

= 11/25 * 100 = 44%

Profit is a general increase in an asset or the value of an asset. If the item's current price is higher than the original purchase price, you will make a profit. For accounting and tax purposes, profits can be categorized in several ways: B. Gross profit and net profit, or realized profit and unrealized (paper) profit.

The definition of victory is profit, benefit, or increase. An example of profit is a 5% increase in income over the past year. An example of a win is a 5 point lead over another team.

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Answer:

answer is the third choice : 104

Step-by-step explanation:

Inscribed Angle Theorem

If an angle is inscribed in a circle, then the measure of the angle equals one half the measure of its intercepted arc.

so the intercepted arc is TWICE the measure of an angle inscribed in a circle

1. A central angle is an angle with endpoints located on a circle's circumference and vertex located at the circle's center. A central angle in a circle determines an arc.

2. An inscribed angle is an angle formed by three points on the circle's circumference.

Angle at the Center Theorem: An inscribed angle is half of the central angle (if they determine the same arc).

In your case angles:

1. ∠QSR is insribed (determines the arc QR);

2. ∠QTR is central (determines the arc QR).

Then by Angle at the Center Theorem, m∠QTR=2m∠QSR=2·52°=104°. Arc QR has the same measure as central angle QSR.

gathmath

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Answer:

D

Step-by-step explanation:

You are looking for what you would need to cancel the yards in 800 yards.

800 yards (1 mile/ 1760 yards).  You have yards in the numerator of your original measurement.  You will cross cancel out the yard on the the top and the yards on the bottom.

Considering the given functions in the graph, we have that:

We look at the graph, and find f(3) and g(3), then add them. Hence:

Then the addition is:

(f + g)(3) = f(3) + g(3) = 0 + 4 = 4.

Same logic, at the graph we have that:

Hence:

(f - g)(1) = f(1) - g(1) = -1 - 1 = -2.

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Answer:

x = 5, 1

Step-by-step explanation:

To solve for x, you must factor the equation. The factored equation will be: (x - 1) (x - 5) = 0. After factoring, isolate the two factored equations: (x - 1) = 0 and (x - 5) = 0. Then solve for x for both the equations which should get you to x = 5, 1.

The expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

The slope at any point of the function can be found by definition of derivative following algebraic handling:

[tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex]

[tex]m = \lim_{h \to 0} \frac{\frac{x+1 - x - h - 1}{(x + h + 1)\cdot (x + 1)} }{h}[/tex]

[tex]m = -\lim_{h\to 0} \frac{1}{(x + h + 1)\cdot (x + 1)}[/tex]

[tex]m = -\frac{1}{(x + 1)^{2}}[/tex]

Thus, the expressions that represent the slope of a tangent to the curve [tex]y = \frac{1}{x+1}[/tex] are [tex]m = \lim_{h \to 0}\frac{\frac{1}{x + h + 1} - \frac{1}{x + 1} }{h}[/tex] and [tex]m = -\frac{1}{(x + 1)^{2}}[/tex], respectively.

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The volume of the cylinder is approximately, 1,539.4 cubic meters.

Volume of a cylinder = πr²h

Given the following:

Diameter of cylinder = 14 m

Radius (r) = 14/2 = 7 m

Height of cylinder = 10 m

Volume of cylinder = πr²h = π(7²)(10)

Volume of cylinder ≈ 1,539.4 cubic meters.

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The probability of at least one of them being a physics instructor is 120 ways to form the committee.

Sometimes, simply the occurrence of the event at least once matters when computing independent events. The "At Least One" Rule is used to describe this. The complement of the probability of the event never occurring will be used to calculate the probability of the event occurring at least once.

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected.

Starting with 6, choose two because we require at least two professors. Let's move on to the remaining 8 individuals (there were initially 10, but now there are just 8): and select 3.

6 select 2; 8 select 3

15×56 =840

We then chose 5 individuals from a group of 10, at least 2 of whom were lecturers.

(9) = 20 options for selecting the professors. 3

(3) = 6 options for selecting the professors.

(9) (¹) = 20 × 6 = 120 ways.

Therefore, 120 ways to form the committee.

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Complete question:

There are five chemistry instructors and six physics instructors at a college. If a committee of four instructors is selected, find the probability of at least one of them being a physics instructor?

There are 120 ways in which 5  riders and 5 horses can be arranged.

We have,

5 riders and 5 horses,

Now,

We know that,

Now,

Using the arrangement formula of Permutation,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

So,

For n = 5,

And,

r = 5

As we have,

n = r,

So,

Now,

Using the above-mentioned formula of arrangement,

i.e.

The total number of ways [tex]^nN_r = \frac{n!}{(n-r)!}[/tex],

Now,

Substituting values,

We get,

[tex]^5N_5 = \frac{5!}{(5-5)!}[/tex]

We get,

The total number of ways of arrangement = 5! = 5 × 4 × 3 × 2 × 1 = 120,

So,

There are 120 ways to arrange horses for riders.

Hence we can say that there are 120 ways in which 5  riders and 5 horses can be arranged.

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The equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

Given the equation; 3[x + 3(4x – 5)] = 15x – 24

We expand and collect like terms

3[x + 3(4x – 5)] = 15x – 24

3( x + 12x - 15 ) = 15x - 24

3x + 36x - 45 = 15x - 24

We add the like terms on both sides

39x - 45 = 15x - 24

Therefore the equivalent equation of the given equation is 39x - 45 = 15x - 24.

Hence, option C) is the correct answer.

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Now you can equate it with second one to get x

Answer:

Substitute y = 3x + 2 into x² - 3x + 2y = -4

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}x^2-3x+2y=-4\\y=3x+2\end{cases}[/tex]

Since y is already isolated in the second equation, the best first step would be to substitute the second equation into the first equation, then solve for x.

Substitute equation 2 into equation 1:

[tex]\implies x^2-3x+2(3x+2)=-4[/tex]

Expand the brackets and simplify so that the equation equals zero:

[tex]\implies x^2-3x+6x+4=-4[/tex]

[tex]\implies x^2+3x+4+4=0[/tex]

[tex]\implies x^2+3x+8=0[/tex]

Now use the Quadratic Formula to solve for x.

Quadratic Formula

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0[/tex]

Define the variables:

[tex]\implies a=1, \quad b=3, \quad c=8[/tex]

Substitute the values into the formula and solve for x:

[tex]\implies x=\dfrac{-3 \pm \sqrt{3^2-4(1)(8)}}{2(1)}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1 \cdot 23}}{2}[/tex]

[tex]\implies x=\dfrac{-3 \pm \sqrt{-1}\sqrt{23}}{2}[/tex]

Remember that [tex]i^2=-1[/tex]

[tex]\implies x=\dfrac{-3 \pm i\sqrt{23}}{2}[/tex]

Therefore, the solutions to the system of equations are:

[tex]x=\dfrac{-3 + i\sqrt{23}}{2}, \quad \dfrac{-3 - i\sqrt{23}}{2}[/tex]

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Answer: 3x - 6 (in^2)

Step-by-step explanation:

base * height / 2

=

3 ( 2x - 4) / 2 (in^2)

= 3x - 6 (in^2)

Answer: 3x-6 in^2

Step-by-step explanation:

There is no way to figure out what x is without additional information, so you have to leave the answer in this form

The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation that shows that 9 is a factor of 72 is given as 9 * 8 = 72

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Answer:

35.5

Step-by-step explanation:

→ Write down the formula

2 × π × r = 222.94

→ Simplify

6.28 × r = 222.94

→ Divide both sides by 6.28

r = 35.5

Answer:

35.5 = r

Step-by-step explanation:

The circumference of a circle is given by

C = 2 * pi *r  where r is the radius

222.94 = 2 * 3.14 * r

222.94 = 6.28 r

Divide each side by 6.28

222.94/6.28 = r

35.5 = r

Answer:

940

Step-by-step explanation:

Since there is a 5 in the ones spot we round the number is the tens spot up by 1: 935 --> 940

Answer:

Step-by-step explanation:

−6m2 18m − 36

= -6(m2 - 3m + 6)

Answer: (0, -7.2)

Step-by-step explanation:

Substituting into point-slope form, the equation is

[tex]y+6=4(x-0.3)[/tex]

The y-intercept is when x=0, so substituting in x=0,

[tex]y+6=4(-0.3)\\\\y+6=-1.2\\\\y=-7.2[/tex]

So, the y-intercept is (0, -7.2).

The equation which represents exponential decay is y=[tex]6(1/3)^{x}[/tex]

Given four equations : 1)y=[tex]3^{x} -4[/tex], 2) y=[tex]2(4)^{x}[/tex], 3) y=[tex]3^{x}/2[/tex], 4) y=[tex]6(1/3)^{x}[/tex].

Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like [tex]a^{x}[/tex].

Decay means when x value increases ,the y value decreases.

We haveto put 3 values for x in the equations to check.

1)y=[tex]3^{x} -4[/tex]

put x=0,y=-3

put x=1, y=-1

put x=2, y=5

No,itdoes not represents exponential decay.

2) y=2[tex]4^{x}[/tex]

put x=0,y=2

put x=1, y=8

put x=2, y=32

No,it does not represents exponential decay.

3) y=[tex]3^{x}/2[/tex]

put x=0,y=0.5

put x=1, y=1.5

put x=2, y=4.5

No,it does not represents exponential decay.

4)y=6[tex](1/3)^{x}[/tex]

put x=0,y=6

put x=1, y=2

put x=2, y=0.67

Yes ,it represents exponential decay.

Hence the equation which represents exponential decay is y=6[tex](1/3)^{x}[/tex].

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Variation is a topic that describes the relationship between or among given variables. So that the expected answers to the questions are;

Variation is a topic that can be used to show the relationship between or among a given number of variables. The types are direct variation, inverse variation, constant variation, and joint variation.

The required answers to the given questions are:

1. y [tex]\alpha[/tex] x

 ⇒ y = kx

where k is the constant of proportionality.

Given that, y = 5 and x =3, then;

5 = 3x

x = [tex]\frac{5}{3}[/tex]

Thus,

y = [tex]\frac{5}{3}[/tex] x

2. v [tex]\alpha[/tex] w

  v = kw

Given: v = 21, w = 8

Then,

21 = 8k

k = [tex]\frac{21}{8}[/tex]

Thus,

v = [tex]\frac{21}{8}[/tex]w

3.  q [tex]\alpha[/tex] [tex]\frac{1}{q}[/tex]

  y = [tex]\frac{k}{q}[/tex]

Given: q = 5, q = 6

Then,

5 = [tex]\frac{k}{6}[/tex]

k = 5 x 6

k = 30

Thus,

p = [tex]\frac{30}{q}[/tex]

4. y [tex]\alpha[/tex] [tex]\frac{1}{x}[/tex]

  y = [tex]\frac{k}{x}[/tex]

Given: y = 11, x = 3

Then,

11 = [tex]\frac{k}{3}[/tex]

k = 11 x 3

k = 33

Thus,

y = [tex]\frac{33}{x}[/tex]

5. F [tex]\alpha[/tex] [tex]\frac{1}{l}[/tex]

F = [tex]\frac{k}{l}[/tex]

Given; F = 20 pounds, l = 1.5 ft

20 = [tex]\frac{k}{1.5}[/tex]

k = 20 x 1.5

k = 30

F = [tex]\frac{30}{l}[/tex]

When l = 6 ft, then;

F = [tex]\frac{30}{6}[/tex]

F  = 5 pounds

The amount of force required is 5 pounds.

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The vectors are linearly independent if and only if k ≠ -11

In mathematics, the definition of a vector is a quantity that is made up of both magnitude and also have direction. This type of quantity is not one that is considered based on its position. A very good example of such a quantity with magnitude and direction is acceleration.

Vectors are used to represent items such as position, velocity, physical quantities and others in mathematics and in physics.

In this question,

We have 2v - 3w

We have to multiply 2 by the values of v and multiply 3 with the values of w

this would produce

[2,6,8]-[6,6,12]

subtract w from v

= [-4, 0, -4]

We u as -1, 0 and 10+k

It is not possible to -1 = 10 + k

-11 = k

Hence we have to conclude that they are linearly independent if and only if k ≠ -11

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The standard error of the estimate of average height in the city is 0.25.

Given average height 64 inches, sample mean and sample standard deviation of 4 inches.

We have to determine the standard error of the estimate of the average height in the city.

Standard error is the error which is predicted before research to happen in research. It is calculated by dividing the standard deviation of the sample by the square root of the sample size.

n=256

μ=mean

s = sample standard deviation

Standard error=s/[tex]\sqrt{n}[/tex]

=4/[tex]\sqrt{256}[/tex]

=4/16

=0.25

Hence the standard error of the estimate of the average height is 0.25.

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Answer:

Step-by-step explanation:

The necessary units conversion can be accomplished by multiplying by appropriate conversion factors. Quantity can be found by multiplying rate by time.

The number of gallons of water produced by melting 1.9 m³ of ice is ...

  [tex]1.9\text{ m$^3$ (ice)}\times\left(\dfrac{100\text{ cm}}{1\text{ m}}\right)^3\times\dfrac{0.92\text{ cm$^3$ (water)}}{1\text{ cm$^3$ (ice)}}\times\dfrac{1\text{ gal}}{3800\text{ cm$^3$}}\\\\=\dfrac{1.9\times10^6\times0.92}{3800}\text{ gal}=\boxed{460\text{ gal}}[/tex]

Multiplying the melting rate by time and converting to height, we have ...

  [tex]\dfrac{179.4\text{ km$^3$}}{1\text{ yr}}\times\dfrac{364\text{ cm}}{1000\text{ km$^3$}}\times6\text{ yr}\approx\boxed{392\text{ cm}}[/tex]

__

Additional comment

The area of the world's oceans is about 361e6 km², so addition of 1000 km³ of water might be expected to increase the water level by (1000/361)e-6 ≈ 2.77e-6 km = 0.277 cm. Something seems a little off in this problem statement.